(174a) Mercury Bioaccumulation Dependence On Aquatic Food Chain Population Dynamics

1. Introduction

Mercury has been recognized as a
global threat to our ecosystem, and it is fast becoming a major concern to
environmentalists and policy makers. Mercury can cycle in the environment in
all media as part of both natural and anthropogenic activities. Once present in
water, mercury is highly dangerous not only to the aquatic communities, but
also to humans through direct and indirect effects [1]. Mercury, mostly in the
form of methyl mercury, accumulates up the aquatic food chains, so that organisms
in higher trophic levels (e.g. fishes) have higher mercury concentrations [2].
As a result, contaminated fish consumption is the most predominant path of
human exposure to mercury.

            It has been
illustrated that a major portion of mercury found in the tissues of various
aquatic organisms enters through food (ingestion). As a consequence, the eating
habits of these organisms are expected to have a significant impact on the
mercury intake by these organisms. The eating habits depend to quite an extend
on the various species populations and their pattern of fluctuations at a given
time in the water body. In ecological literature, these different patterns are referred
to as regimes. A regime, therefore, if maintained for sufficient duration, is
expected to affect the steady state mercury bioaccumulation levels in different
species. As a result, manipulation of the regimes of these species populations
presents a tool to control mercury bioaccumulation levels.

            This work performs an
optimal control analysis to achieve regime shifts in a predator-prey model and
analyzes these regime shifts from mercury bioaccumulation point of view. The predator-prey
model, known as the Canale's model, models three species and nutrients in a
water body. Mercury bioaccumulation along the food chain is modeled using a
bioenergetics model that accounts for mercury intake through water as well as
ingestion (food). The predator-prey model and the bioenergetics model are
connected by correlating the food intake (and hence the mercury intake) of a
particular species with the current population of the prey for that species.
Thus, any fluctuations in the species populations reflect in the varying
mercury bioaccumulation in those species.

2. Models

The
predator-prey model analyzed in this work in an extension of the three-species
predator prey model, know as the Rosenzweig?MacArthur model [3]. The Rosenzweig?MacArthur
tritrophic food chain model comprises of three species, called as the prey,
predator and super-predator, which are modeled using a set of ordinary
differential equations. This model is complemented by an extra differential
equation for the nutrient. Such an equation is simply the balance of the
various flows regulating the nutrient concentration, namely inflow and outflow rates,
nutrient recycling due to decomposition of dead individuals of the three
populations and nutrient uptake rate of the prey population. This resulting
model is referred to as the Canale's model is this work. The model has been
extensively studied in bifurcation literature, and a detailed exposition of
this model can be found in those reference [3, 4].

            Estimating metal
bioaccumulation in organisms has been a topic of intense research. Since the
actual bioaccumulation of a metal (such as mercury) along a food chain depends
to quite an extent on the site specific conditions, a generalized model to
predict metal bioaccumulation has been difficult to formulate. Out of the
various types of models that have been proposed, the bioenergetics based toxicokinetic
models, which are a type of general kinetic models, have been quite promising [5].
The bioenergetics based models are appropriate to model mercury bioaccumulation
since they model the metal intake through water as well as food, and the model
parameters are relatively easy to determine. The basic equation that is
applicable to each species is the simple unsteady state mass balance equation
where accumulation (of mercury) in a species is the difference between the sum
of the total input and total generation and sum of the total output and total
consumption. It assumes that mercury uptake is proportional to the flux, and
uses uptake parameters such as food rate and assimilation efficiency for
computation. Certain assumptions of the model are: elimination is not related
to organism's metabolism, equation parameters are assumed to be constant, and physiological
parameters are known. A detailed explanation of the bioenergetics model can be
found in [5]. Various studies have been conducted to estimate different model
parameters specific to mercury [6, 7]. In this work, the literature has been
reviewed and published data has been used to identify appropriate model
parameters.

            The predator-prey
model and the bioaccumulation model are inter-related by correlating the food
intake of any particular species with the mercury intake for the
bioaccumulation model. Changes in the dynamics of the Canale's model change the
instantaneous food intake for the predators and super-predators (due to
changing predation rates). This affects the total mercury that is taken by these
species through food. Hence, any regime shift in the predator-prey model, which
affects the predation rates, affects the mercury intake by the species. If the
particular regime is maintained for a sufficient duration, the steady state
mercury concentration in these species can alter. This is the basic foundation
for the proposed work.

3. Regime change and optimal
control

Optimal control theory presents
an option to derive time dependent management strategies that can effectively
achieve regime shifts in food chain models. Past work by the authors has
illustrated the success of this approach [8, 9].  That work uses Fisher
information based sustainability hypothesis, proposed by Cabezas and Fath [10],
to formulate time dependent objective functions for the control problem. A
similar approach has been used in this work. The regime shift is to be achieved
by minimizing the variation of the time averaged Fisher information around the
constant Fisher information of the targeted regime. More information about this
approach can be found in [8, 9].

Canale's model
exhibits various regimes such as cyclic low frequency, cyclic high frequency,
stationary, chaotic etc. [3]. The idea proposed in this work is to achieve
regime shift from a regime leading to high mercury bioaccumulation to a regime
resulting in low mercury bioaccumulation. The control variables to achieve the
regime shift are: nutrient inflow rate and nutrient input concentration.

4. Results and discussion

Simulations for the integrated
model (Canale's model and the bioaccumulation model) illustrate that there is a
strong correlation between the regime and steady state mercury bioaccumulation
in predator and super-predators. Hence, the objective of causing a regime
change in justified.

The solution of
various control problems indicate that the some regime shifts are easily
achievable, while others are quite difficult to achieve. Preliminary studies
show that shifting the model from low bioaccumulation to high bioaccumulation
regime is possible. This, however, is not the desired change. Attempts to cause
shift from higher bioaccumulation to lower bioaccumulation regime led to mixed
results. This emphasizes the severe nonlinearities in these population models,
and thereby highlighting the fact that a systematic study of these issues is
essential.

Further
investigations in this field are expected to put forth various possibilities
that might exist to effectively achieve stable population dynamics, while at
the same time achieve reduced mercury bioaccumulation levels in the aquatic
species.

References

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